The instant invention relates to wedge analysis in general and, more particularly, to a method for performing wedge analysis for assessing wedge instabilities in underground openings, such as mines, caves, and the like.
The stability of joint defined wedges in the backs of underground openings, such as mines, is a key concern for support design. Assessments of roof support typically demand consideration of the primary or average orientations of ubiquitous structure (sets or oriented clusters of joints or shear swarms) within the rockmass. These representative sets are then examined for mutual intersections that form wedges which, in turn, are assumed to reach a maximum dimension limited only by the span, assuming full continuity and complete ubiquity of the structure. This full-span or ubiquitous wedge analysis approach typically represents a worst-case analysis and often leads to highly conservative support design recommendations. That is, the worst-case ground support design would be based on the presumption of an existing full-span wedge, or on the largest wedge that can form across a given span from the intersection of ubiquitous structure, resulting in a design that is both overly conservative and costly.
In most cases, however, the probability of occurrence of three or more joints mutually intersecting to create a full-span wedge is low, due to the discontinuous nature of joints and the variability of spacing. In addition, any discrete wedges which do form may possess internal stability due to clamping or to tensile strength of rock bridges. This reduced likelihood of full-span wedge formation and instability is reflected in FIGS. 1A and 1B. In FIG. 1A, full-span wedge analysis predictions are shown, based on available jointing at three mine sites. These wedge analysis predictions are large steep wedges.
FIG. 1B which illustrates the actual groundfall data shows that the maximum relative wedge heights (and therefore the wedge volumes) are significantly reduced compared to those predicted by full-span wedge analysis. The reasons for this reduction include limited joint persistence and finite spacings as well as the stabilizing impact of confinement on steep wedges. See Diederichs, M. et al., Tensile Strength and Abutment Relaxation as Failure Control Mechanisms in Underground Excavations, Int. J. Rock Mech. Min. Sci. and Geomech. Abstr., vol. 36, pp. 69-96, 1999; Brady, B. et al., Rock Mechanics for Underground Mining, Chapman and Hall, 1993; and Sofianos, A., Stability of Rock Wedges in Tunnel Roofs, Int. J. Rock Mech. Min. Sci. and Geomech. Abstr., vol. 23, no. 2, pp. 119-130, 1986.
In sum, full-span ubiquitous wedge analysis tends to over-predict the support demand (capacity requirements) for underground excavations in rock. The real demand is lower due to the probability of full-span wedge formation and due to the inherent capacity of the joints.
Accordingly, a need exists for a wedge analysis method for scaling full-span wedge predictions, accounting for both occurrence and instability potential of possible wedge geometries.
A need also exists for a wedge analysis method for generating predictions for wedge failure potential and support demand to result in more economical support design for wedges to be provided in underground openings, such as mines, caves, and the like.
There is provided a method for performing wedge analysis for assessing the likelihood of wedge occurrence and instability in underground openings, such as mines, caves, and the like. The method scales full-span wedge predictions by accounting for both occurrence and instability potential of possible wedge geometries. The method allows for optimization of ground support design, which is currently based on conservative standards, through bolt length reduction or bolt pattern spacing increase, thereby reducing the overall support costs. Overall, the method generates predictions for wedge failure potential and support demand to result in more economical support design for wedges.
The method is referred to herein as the viability index approach. The viability index approach uses joint set dominance, spacing, and trace length to factor full-span predictions for wedge size, accounting implicitly for the likelihood of wedge occurrence. The viability index approach also accounts for the likelihood of wedge instability, based on joint roughness, shape and alteration, as well as wedge shape and clamping stress, to reduce the required support demand.
The viability index approach or method for performing wedge analysis for assessing wedge instabilities of wedges in an underground opening, according to the present disclosure, includes the steps of: determining an occurrence index, Io, quantifying a potential for wedge formation in the underground opening for each of the wedges; determining an instability index, Is, describing a potential for structurally bounded wedges of the underground opening to be unstable for each of the wedges; and determining a viability index by determining the square root of the product of the occurrence and instability indices for each of the wedges, wherein the viability index indicates a probability of failure of a wedge.
The viability index approach is a useful technique for optimizing support designs, currently based on conservative standards, through bolt length reduction or pattern spacing increase, thereby reducing operating costs.